122 THE SCIENTIFIC PAPERS OF 



occasional variation of speed is to be 1 per cent., and that the 

 dimensions of the cup are as follows, 



Diameter at upper rim . . . = 200 millims. 



Diameter of rim above the liquid . . = 200 millims. 



Diameter of orifice at bottom of cup . = 90 millims. 

 we find the available power of the instrument in the following 

 manner : 



The normal speed of a cup of these dimensions is, according to 

 our formula. 



= 3-31 revolutions per 



second. 



The height to which the liquid is raised by rotation increases in 

 the square ratio of the speed of rotation, the increase of height 

 due to 1 per cent, increase of speed would therefore result from 

 the following proportion, 100 v : 101 v = ,Jh : JR, or the height 

 due to the increased speed, ti = 204 millims., that is to say, the 

 liquid would be raised 4 millims. above the brim of the cup, 

 which, being an unbalanced column, will produce an upward flow 

 of the liquid in the cup, as expressed by the well-known formula, 

 v = ftgh ; or h being in this case = 4 millims., we have v = *280 

 metre flow per second, which, if multiplied by the least sectional 

 area at the entrance into the cup = "0057 square metre, gives 

 the quantity of liquid '280 metre x '0057 square metre = '0016 

 cubic metre, or r.6 litre of liquid raised 204 millims. high and 

 projected with a velocity of \%^ x 3*31 x 27ir = 2*1 metres per second 

 over the brim of the cup, to be stopped by the stationary wings 

 and once more accelerated by the rotating wings, which, being 

 one-fifth more in diameter than the cup itself, impart to the 

 liquid a velocity of f x 2'1 = 2'5 metres per second. These accele- 



v n - 

 rations represent a power which, according to the formula h =-x-, 



*9 

 is equal to the same liquid being lifted 



for v = 2*1 metres . to '225 metre height, 



. and for v = 2'5 . . to "320 metre height. 



In the cup it was lifted to '200 metre height, 



making a total lift . to '745 metre height. 



